Weak statistical convergence and weak filter convergence for unbounded sequences

Kadets V., Leonov A., ORHAN C.

Journal of Mathematical Analysis and Applications, vol.371, no.2, pp.414-424, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 371 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/j.jmaa.2010.05.031
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.414-424
  • Keywords: Banach space, Filter, Statistical convergence, Weak topology
  • Ankara University Affiliated: Yes

Abstract

For every weakly statistically convergent sequence (xn) with increasing norms in a Hilbert space we prove that supn{short parallel}xn{short parallel}/√n < ∞. This estimate is sharp. We study analogous problem for some other types of weak filter convergence, in particular for the Erdös-Ulam filters, analytical P-filters and Fσ filters. We present also a refinement of the recent Aron-Garcia-Maestre result on weakly dense sequences that tend to infinity in norm. © 2010 Elsevier Inc.